Characterization of diffusion processes: Normal and anomalous regimes

Samuel B. Alves, Gilson F. de Oliveira, Luimar C. de Oliveira, Thierry Passerat de Silans, Martine Chevrollier, Marcos Oriá and Hugo L.D. de S. Cavalcante

Physica A: Statistical Mechanics and its Applications, 2016, vol. 447, issue C, 392-401

Abstract: Many man-made and natural processes involve the diffusion of microscopic particles subject to random or chaotic, random-like movements. Besides the normal diffusion characterized by a Gaussian probability density function, whose variance increases linearly in time, so-called anomalous-diffusion regimes can also take place. They are characterized by a variance growing slower (subdiffusive) or faster (superdiffusive) than normal. In fact, many different underlying processes can lead to anomalous diffusion, with qualitative differences between mechanisms producing subdiffusion and mechanisms resulting in superdiffusion. Thus, a general description, encompassing all three regimes and where the specific mechanisms of each system are not explicit, is desirable. Here, our goal is to present a simple method of data analysis that enables one to characterize a model-less diffusion process from data observation, by observing the temporal evolution of the particle spread. To generate diffusive processes in different regimes, we use a Monte-Carlo routine in which both the step-size and the time-delay of the diffusing particles follow Pareto (inverse-power law) distributions, with either finite or diverging statistical momenta. We discuss on the application of this method to real systems.

Keywords: Anomalous diffusion; Lévy flights; Subdiffusion and superdiffusion (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:447:y:2016:i:c:p:392-401

DOI: 10.1016/j.physa.2015.12.049

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